Parameters

Characteristics

• OID:
  1.3.132.0.5
• j-invariant:
  3925759440046949401308357014943784
• Trace of Frobenius:
  -148884003161464613
• Discriminant:
  3040591781815807764515357141309519

SAGE

F.<x> = GF(2)[]
K = GF(2^113, name="x", modulus=u^113 +  u^9 + 1)
E = EllipticCurve(K, (1, K.from_integer(0x00689918dbec7e5a0dd6dfc0aa55c7), 0, 0, K.from_integer(0x0095e9a9ec9b297bd4bf36e059184f)))
E.set_order(0x010000000000000108789b2496af93 * 0x2)
G = E(K.from_integer(0x01a57a6a7b26ca5ef52fcdb8164797), K.from_integer(0x00b3adc94ed1fe674c06e695baba1d))

JSON

{
  "name": "sect113r2",
  "desc": "",
  "oid": "1.3.132.0.5",
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 113,
    "poly": [
      {
        "power": 113,
        "coeff": "0x01"
      },
      {
        "power": 9,
        "coeff": "0x01"
      },
      {
        "power": 0,
        "coeff": "0x01"
      }
    ],
    "degree": 113,
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0x00689918dbec7e5a0dd6dfc0aa55c7"
    },
    "b": {
      "raw": "0x0095e9a9ec9b297bd4bf36e059184f"
    }
  },
  "generator": {
    "x": {
      "raw": "0x01a57a6a7b26ca5ef52fcdb8164797"
    },
    "y": {
      "raw": "0x00b3adc94ed1fe674c06e695baba1d"
    }
  },
  "order": "0x010000000000000108789b2496af93",
  "cofactor": "0x2",
  "characteristics": {
    "discriminant": "3040591781815807764515357141309519",
    "j_invariant": "3925759440046949401308357014943784",
    "trace_of_frobenius": "-148884003161464613"
  }
}